This is not going to happen automatically in Word. There is no switch or command that will make this happen.

I am a lawyer. I have been using Word for more than 20 years. I seldom use line numbering. I would not attempt to do what you want. I would use Word's Track Changes features. If you print the result document showing changes, it is easy enough to follow and see what was changed and where.

You might be able to get something like what you are requesting by saving your document as a pdf and then converting the pdf back to Word (requires Word 2013 or later or a third-party application). This will give you something that is incredibly difficult to edit but the line numbers will no longer automatically shift.